Answer
neither even nor odd.
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$
We know that if a function is eben, then $f(-x)=f(x).$
Hence we plug in $-x$ to see what happens.
$f(-x)=1-(-x)+(-x)^3=1+x-x^3.$ This is neither $f(x)$ nor $f(-x)$, hence the function is neither even nor odd.